How does the radius affect frictional force in circular motion?

[HaoPhysics]

Homework Statement

A car drives along a curved track. The frictional force exerted by the track on the car is:

a. greater than the frictional force exerted by the car on the track
b. directed radially outward
c. opposite in direction to the frictional force exerted by the car on the track
d. zero if the car's speed is constant
e. dependent on the radius of the track

Homework Equations

mV²/R = Centripetal force
F_fr = F_c if the car is to not slide

The Attempt at a Solution

So the track must exert a frictional force on the car equal to its centripetal force as it rounds the circle to prevent it from slipping. And this centripetal force is dependent on the radius of the track R.

So from this I think the answer could be E.

But also, between any two objects A and B, the friction A exerts on B is equal and opposite in direction to the frictional force B exerts on A.

So from this I think the answer could be C.

The book says the answer is C. But I want to know why it can't be E.

 

[kuruman]

E is also a correct answer.

But I want to know why it can't be E.

Because the book says so. Seriously, though, E looks correct to me because the force of static friction needed is $f_s=\frac{mv^2}{R}$. Of course it also depends on the speed and mass of the car, not only on the radius of the track, but I don't see an "only" in E.

 

[HaoPhysics]

E is also a correct answer.

Because the book says so. Seriously, though, E looks correct to me because the force of static friction needed is $f_s=\frac{mv^2}{R}$. Of course it also depends on the speed and mass of the car, not only on the radius of the track, but I don't see an "only" in E.

Thanks for the input! And yes, I feel that a part of the secondary education program is learning to question the books.

 

[CWatters]

E is badly worded? The friction force is inversely dependent/proportional on the radius.

 

[kuruman]

Thanks for the input! And yes, I feel that a part of the secondary education program is learning to question the books.

Not just the books. Question everything.

 

[HaoPhysics]

E is badly worded? The friction force is inversely dependent/proportional on the radius.

That is also a good point.

 

[HaoPhysics]

Not just the books. Question everything.

Very true. I like your signature quote.

 

[kuruman]

E is badly worded? The friction force is inversely dependent on the radius.

In my understanding, "dependent" could possibly mean linearly, inversely, inversely squared, exponentially, whatever. As long as there is a "radius" (independent variable) on the right side, the force of friction (dependent variable) is "dependent" regardless the functional form. If the author of the question meant "directly proportional", then it is a poorly phrased question. Again in my opinion.